Re: Fractal Dimension Computation in Python Code

On Friday, September 29, 2000 at 12:45:00 PM UTC+5:45, Mike Brenner wrote: > Myk> ... Has anyone got a fast routine for calculating the fractal > dimension of a set of points in 2 or 3D space? Thanks. > > According to the inventor of fractals (Hausdorff in the year 1899), you >

Re: Writing a program to illustrate a fractal

On 8/26/18 5:40 PM, Dennis Lee Bieber wrote: > But their definition is still confusing as it is formulated with a > expression as the argument to a(). > > Taken literally, it says for n+4 to call a() with an argument of 8 (2n) > AND to call it with an argument of 7 (2n-1) (returning two

Re: Writing a program to illustrate a fractal

On Sunday, August 26, 2018 at 3:13:00 PM UTC-5, Oscar Benjamin wrote: > On Sun, 26 Aug 2018 at 20:52, Musatov wrote: > > > > Thank you, Richard. If anyone is interested further, even in writing a > > Python code to generate the sequence or further preparing of an animation I > > would be delight

Re: Writing a program to illustrate a fractal

On Sun, 26 Aug 2018 at 20:52, Musatov wrote: > > Thank you, Richard. If anyone is interested further, even in writing a Python > code to generate the sequence or further preparing of an animation I would be > delighted. It would not take long to write code to plot your sequence if you first cov

Re: Writing a program to illustrate a fractal

> >>>> > >>>> For 1 <= n <= 3, a(n) = n; thereafter, a(2n) = a(n) + a(n+1), a(2n-1) = > >>>> a(n) + a(n-2). > > >>> I am not sure what 'fractal' property this sequence has that he > >>> wants to > >&g

Re: Writing a program to illustrate a fractal

(n) + a(n+1), a(2n-1) = >>>> a(n) + a(n-2). >>> I am not sure what 'fractal' property this sequence has that he >>> wants to >> display. > I'm sorry, let me try to explain: > > Here is my output: > 1, 2, 3, 5, 4, 8, 7, 9, 7, 12, 13,

Re: Writing a program to illustrate a fractal

o, it is not a strict function. I'd also write it > > as > > I think they intend that a(n) is defined for n being an integer (or > maybe just the Natural Numbers, since it isn't defined for values below 1) > > The two provided definitions provide the recursive defini

Re: Writing a program to illustrate a fractal

> returning TWO values? If so, it is not a strict function. I'd also write it > as I think they intend that a(n) is defined for n being an integer (or maybe just the Natural Numbers, since it isn't defined for values below 1) The two provided definitions provide the recursive defini

Writing a program to illustrate a fractal

I have an integer sequence of a fractal nature and want to know if it is possible to write a program to illustrate it in a manner similar to the many animated Mandelbrot illustrations. The sequence is defined by: For 1 <= n <= 3, a(n) = n; thereafter, a(2n) = a(n) + a(n+1), a(2n-1) = a(n

Re: Fractal

On Thu, May 16, 2013 at 10:55 AM, Sharon COUKA wrote: > # Register events > c.bind('i', zoom) > c.bind('i', unzoom) > c.bind('i', mouseMove) I'm not an expert at Tkinter so maybe one of the other residents can help you better with that. The code above looks wrong to me, though. As far as I know,

Re: Fractal

On Thu, May 16, 2013 at 5:04 AM, Sharon COUKA wrote: > I have to write the script, and i have one but the zoom does not work That doesn't answer my question. Perhaps if you would share with us what you already have, then we could point out what you need to do and where to get your "zoom" working

Re: Fractal

On Thu, May 16, 2013 at 5:11 PM, Ulrich Eckhardt wrote: > Am 16.05.2013 02:00, schrieb alex23: > >> My favourite is this one: >> >> http://preshing.com/20110926/high-resolution-mandelbrot-in-obfuscated-python > > > Not only is this blog entry an interesting piece of art, there's other > interestin

Re: Fractal

Am 16.05.2013 02:00, schrieb alex23: My favourite is this one: http://preshing.com/20110926/high-resolution-mandelbrot-in-obfuscated-python Not only is this blog entry an interesting piece of art, there's other interesting things to read there, too. Thanks! Uli -- http://mail.python.org/m

Re: Fractal

On May 15, 10:07 pm, "Colin J. Williams" wrote: > Google is your friend.  Try "Mandelbrot Python" My favourite is this one: http://preshing.com/20110926/high-resolution-mandelbrot-in-obfuscated-python -- http://mail.python.org/mailman/listinfo/python-list

Re: Fractal

On Mon, May 13, 2013 at 9:41 AM, Sharon COUKA wrote: > Hello, I'm new to python and i have to make a Mandelbrot fractal image for > school but I don't know how to zoom in my image. > Thank you for helping me. Is this a GUI application or does it just write the image to a fil

Re: Fractal

On 2013-05-13, Sharon COUKA wrote: > Hello, I'm new to python and i have to make a Mandelbrot fractal image for > school but I don't know how to zoom in my image. > Thank you for helping me. It's a fractal image, so you zoom in/out with the following Python instruction:

Re: Fractal

On 13/05/2013 11:41 AM, Sharon COUKA wrote: Hello, I'm new to python and i have to make a Mandelbrot fractal image for school but I don't know how to zoom in my image. Thank you for helping me. Envoyé de mon iPad Google is your friend. Try "Mandelbrot Python"

Fractal

Hello, I'm new to python and i have to make a Mandelbrot fractal image for school but I don't know how to zoom in my image. Thank you for helping me. Envoyé de mon iPad -- http://mail.python.org/mailman/listinfo/python-list

Re: Measuring Fractal Dimension ?

On Jun 29, 3:17 am, greg wrote: > Paul Rubin wrote: > > Steven D'Aprano writes: > > >>But that depends on what you call "things"... if electron shells are real > >>(and they seem to be) and discontinuous, and the shells are predicted/ > >>specified by eigenvalues of some continuous function, is t

Re: Measuring Fractal Dimension ?

greg wrote: Steven D'Aprano wrote: one minute the grenade is sitting there, stable as can be, the next it's an expanding cloud of gas and metal fragments. I'm not sure that counts as "discontinuous" in the mathematical sense. If you were to film the grenade exploding and play it back slowly en

Re: Measuring Fractal Dimension ?

Paul Rubin wrote: Steven D'Aprano writes: But that depends on what you call "things"... if electron shells are real (and they seem to be) and discontinuous, and the shells are predicted/ specified by eigenvalues of some continuous function, is the continuous function part of nature or just a

Re: Measuring Fractal Dimension ?

Steven D'Aprano wrote: one minute the grenade is sitting there, stable as can be, the next it's an expanding cloud of gas and metal fragments. I'm not sure that counts as "discontinuous" in the mathematical sense. If you were to film the grenade exploding and play it back slowly enough, the pr

Re: Measuring Fractal Dimension ?

Steven D'Aprano writes: > But that depends on what you call "things"... if electron shells are real > (and they seem to be) and discontinuous, and the shells are predicted/ > specified by eigenvalues of some continuous function, is the continuous > function part of nature or just a theoretical a

Re: Measuring Fractal Dimension ?

On Sun, 28 Jun 2009 03:28:51 -0700, Paul Rubin wrote: > Steven D'Aprano writes: >> I thought we were talking about discontinuities in *nature*, not in >> mathematics. There's no "of course" about it. > > IIRC we were talking about fractals, which are a topic in mathematics. > This led to some di

Re: Measuring Fractal Dimension ?

Steven D'Aprano writes: > I thought we were talking about discontinuities in *nature*, not in > mathematics. There's no "of course" about it. IIRC we were talking about fractals, which are a topic in mathematics. This led to some discussion of mathematical continuity, and the claim that mathemat

Re: Measuring Fractal Dimension ?

On Sat, 27 Jun 2009 23:52:02 -0700, Paul Rubin wrote: > Steven D'Aprano writes: >> Depends on how you define "discontinuous". > > The mathematical way, of course. For any epsilon > 0, etc. I thought we were talking about discontinuities in *nature*, not in mathematics. There's no "of course"

Re: Measuring Fractal Dimension ?

Steven D'Aprano writes: > Depends on how you define "discontinuous". The mathematical way, of course. For any epsilon > 0, etc. > Catastrophe theory is full of discontinuous changes in state. Animal > (by which I include human) behaviour often displays discontinuous > changes. So does chemist

Re: Measuring Fractal Dimension ?

On Thu, 25 Jun 2009 12:23:07 +0100, Robin Becker wrote: > Paul Rubin wrote: [...] >> No really, it is just set theory, which is a pretty bogus subject in >> some sense. There aren't many discontinuous functions in nature. Depends on how you define "discontinuous". Catastrophe theory is full of

Re: Measuring Fractal Dimension ?

Robin Becker writes: > > There is a philosophy of mathematics (intuitionism) that says... > > there are NO discontinuous functions. > so does this render all the discreteness implied by quantum theory > unreliable? or is it that we just cannot see(measure) the continuity > that really happens?

Re: Measuring Fractal Dimension ?

On Jun 25, 10:38 am, Paul Rubin wrote: > Robin Becker writes: > > someone once explained to me that the set of systems that are > > continuous in the calculus sense was of measure zero in the set of all > > systems I think it was a fairly formal discussion, but my >

Re: Measuring Fractal Dimension ?

On Jun 25, 12:23 pm, Robin Becker wrote: > Paul Rubin wrote: > > so does this render all the discreteness implied by quantum theory unreliable? > or is it that we just cannot see(measure) the continuity that really happens? > Certainly there are people like Wolfram who seem to think we're in some

Re: Measuring Fractal Dimension ?

Paul Rubin wrote: . That is very straightforward if you don't mind a handwave. Let S be some arbitrary subset of the reals, and let f(x)=0 if x is in S, and 1 otherwise (this is a discontinuous function if S is nonempty). How many different such f's can there be? Obviously one for ever

Re: Measuring Fractal Dimension ?

Robin Becker writes: > someone once explained to me that the set of systems that are > continuous in the calculus sense was of measure zero in the set of all > systems I think it was a fairly formal discussion, but my > understanding was of the hand waving sort. That is very straightforward if yo

Re: Measuring Fractal Dimension ?

pdpi wrote: ... But yeah, Log2 and LogE are the only two bases that make "natural" sense except in specialized contexts. Base 10 (and, therefore, Log10) is an artifact of having that 10 fingers (in fact, whatever base you use, you always refer to it as base 10). someone once explained to m

Re: Measuring Fractal Dimension ?

On Jun 24, 1:32 pm, Mark Dickinson wrote: > On Jun 24, 10:12 am, pdpi wrote: > > > Regarding inf ** 0, why does IEEE745 define it as 1, when there is a > > perfectly fine NaN value? > > Other links:  the IEEE 754 revision working group mailing list > archives are public;  there was extensive disc

Re: Measuring Fractal Dimension ?

On Jun 24, 2:58 pm, "Hendrik van Rooyen" wrote: > "Steven D'Aprano" wrote: > >On Mon, 22 Jun 2009 13:43:19 -0500, David C. Ullrich wrote: > > >> In my universe the standard definition of "log" is different froim what > >> log means in a calculus class > > >Now I'm curious what the difference is.

Re: Measuring Fractal Dimension ?

"Steven D'Aprano" wrote: >On Mon, 22 Jun 2009 13:43:19 -0500, David C. Ullrich wrote: > >> In my universe the standard definition of "log" is different froim what >> log means in a calculus class > >Now I'm curious what the difference is. > Maybe he is a lumberjack, and quite all right... - He

Re: Measuring Fractal Dimension ?

On Jun 24, 10:12 am, pdpi wrote: > Regarding inf ** 0, why does IEEE745 define it as 1, when there is a > perfectly fine NaN value? Other links: the IEEE 754 revision working group mailing list archives are public; there was extensive discussion about special values of pow and similar functions

Re: Measuring Fractal Dimension ?

On Mon, 22 Jun 2009 13:43:19 -0500, David C. Ullrich wrote: > In my universe the standard definition of "log" is different froim what > log means in a calculus class Now I'm curious what the difference is. -- Steven -- http://mail.python.org/mailman/listinfo/python-list

Re: Measuring Fractal Dimension ?

On Jun 24, 10:12 am, pdpi wrote: > Regarding inf ** 0, why does IEEE745 define it as 1, when there is a > perfectly fine NaN value? Have a look at: http://www.eecs.berkeley.edu/~wkahan/ieee754status/ieee754.ps (see particularly page 9). Mark -- http://mail.python.org/mailman/listinfo/python-l

Re: Measuring Fractal Dimension ?

On Jun 23, 6:49 pm, Lie Ryan wrote: > Mark Dickinson wrote: > > On Jun 23, 3:52 am, Steven D'Aprano > > wrote: > >> On Mon, 22 Jun 2009 13:43:19 -0500, David C. Ullrich wrote: > >>> In my universe the standard definition of "log" is different froim what > >>> log means in a calculus class > >> No

Re: Measuring Fractal Dimension ?

In article , Mark Dickinson wrote: >On Jun 22, 7:43=A0pm, David C. Ullrich wrote: >> >> Surely you don't say a curve is a subset of the plane and >> also talk about the integrals of verctor fields over _curves_? >> [snip rest of long response that needs a decent reply, but >> possibly not here.

Re: Measuring Fractal Dimension ?

Mark Dickinson wrote: > On Jun 23, 3:52 am, Steven D'Aprano > wrote: >> On Mon, 22 Jun 2009 13:43:19 -0500, David C. Ullrich wrote: >>> In my universe the standard definition of "log" is different froim what >>> log means in a calculus class >> Now I'm curious what the difference is. > > It's jus

Re: Measuring Fractal Dimension ?

On Jun 23, 3:52 am, Steven D'Aprano wrote: > On Mon, 22 Jun 2009 13:43:19 -0500, David C. Ullrich wrote: > > In my universe the standard definition of "log" is different froim what > > log means in a calculus class > > Now I'm curious what the difference is. It's just the usual argument about whe

Re: Measuring Fractal Dimension ?

On Jun 22, 2009, at 2:16 PM, David C. Ullrich wrote: On Mon, 22 Jun 2009 10:31:26 -0400, Charles Yeomans wrote: On Jun 22, 2009, at 8:46 AM, pdpi wrote: On Jun 19, 8:13 pm, Charles Yeomans wrote: On Jun 19, 2009, at 2:43 PM, David C. Ullrich wrote: Hmm. You left out a bit in the

Re: Measuring Fractal Dimension ?

On Jun 22, 7:43 pm, David C. Ullrich wrote: > Surely you don't say a curve is a subset of the plane and > also talk about the integrals of verctor fields over _curves_? > [snip rest of long response that needs a decent reply, but > possibly not here... ] I wonder whether we can find a better pl

Re: Measuring Fractal Dimension ?

On Fri, 19 Jun 2009 12:40:36 -0700 (PDT), Mark Dickinson wrote: >On Jun 19, 7:43 pm, David C. Ullrich wrote: >> Evidently my posts are appearing, since I see replies. >> I guess the question of why I don't see the posts themselves >> \is ot here... > >Judging by this thread, I'm not sure that mu

Re: Measuring Fractal Dimension ?

On Mon, 22 Jun 2009 10:31:26 -0400, Charles Yeomans wrote: > >On Jun 22, 2009, at 8:46 AM, pdpi wrote: > >> On Jun 19, 8:13 pm, Charles Yeomans wrote: >>> On Jun 19, 2009, at 2:43 PM, David C. Ullrich wrote: >>> >>> >>> >>> >>> >>> Hmm. You left out a bit in the first definition you cite:

Re: Measuring Fractal Dimension ?

 So I've been getting it wrong all this time.  Oh well, >> >> at least I'm not alone: >> >> >> "De?nition 1. A simple closed curve J, also called a >> >> Jordan curve, is the image of a continuous one-to-one >> >> funct

Re: Measuring Fractal Dimension ?

On Jun 22, 2009, at 8:46 AM, pdpi wrote: On Jun 19, 8:13 pm, Charles Yeomans wrote: On Jun 19, 2009, at 2:43 PM, David C. Ullrich wrote: Hmm. You left out a bit in the first definition you cite: "A simple closed curve J, also called a Jordan curve, is the image of a continuous one-t

Re: Measuring Fractal Dimension ?

alled a > >> Jordan curve, is the image of a continuous one-to-one > >> function from R/Z to R2. [...]" > > >> - Tom Hales, in 'Jordan's Proof of the Jordan Curve Theorem'. > > >> "We say that Gamma is a curve if it is the image in

Re: Measuring Fractal Dimension ?

On Jun 18, 2009, at 2:21 PM, David C. Ullrich wrote: On Wed, 17 Jun 2009 05:46:22 -0700 (PDT), Mark Dickinson wrote: On Jun 17, 1:26 pm, Jaime Fernandez del Rio wrote: On Wed, Jun 17, 2009 at 1:52 PM, Mark Dickinson wrote: Maybe James is thinking of the standard theorem that says that if

Re: Measuring Fractal Dimension ?

On Wed, 17 Jun 2009 05:46:22 -0700 (PDT), Mark Dickinson wrote: >On Jun 17, 1:26 pm, Jaime Fernandez del Rio >wrote: >> On Wed, Jun 17, 2009 at 1:52 PM, Mark Dickinson wrote: >> > Maybe James is thinking of the standard theorem >> > that says that if a sequence of continuous functions >> > on an

Re: Measuring Fractal Dimension ?

Mark Dickinson writes: > It looks as though you're treating (a portion of?) the Koch curve as > the graph of a function f from R -> R and claiming that f is > uniformly continuous. But the Koch curve isn't such a graph (it > fails the 'vertical line test', I think you treat it as a function f: R

Re: Measuring Fractal Dimension ?

On Jun 17, 1:26 pm, Jaime Fernandez del Rio wrote: > P.S. The snowflake curve, on the other hand, is uniformly continuous, right? The definition of uniform continuity is that, for any epsilon > 0, there is a delta > 0 such that, for any x and y, if x-y < delta, f(x)-f (y) < epsilon. Given that K

Re: Measuring Fractal Dimension ?

On Jun 17, 12:52 pm, Mark Dickinson wrote: > g_n(t) = nt if 0 <= t <= 1/n else 1 Whoops. Wrong definition. That should be: g_n(t) = nt if 0 <= t <= 1/n else n(2/n-t) if 1/n <= t <= 2/n else 0 Then my claim that g_n(t) -> 0 for all t might actually make sense... -- http://mail.python

Re: Measuring Fractal Dimension ?

On Jun 19, 7:43 pm, David C. Ullrich wrote: > Evidently my posts are appearing, since I see replies. > I guess the question of why I don't see the posts themselves > \is ot here... Judging by this thread, I'm not sure that much is off-topic here. :-) > Perhaps not. I'm very surprised to see tho

Re: Measuring Fractal Dimension ?

ales, in 'Jordan's Proof of the Jordan Curve Theorem'. "We say that Gamma is a curve if it is the image in the plane or in space of an interval [a, b] of real numbers of a continuous function gamma." - Claude Tricot, 'Curves and Fractal Dimension' (Springer, 19

Re: Measuring Fractal Dimension ?

, is the image of a continuous one-to-one >function from R/Z to R2. [...]" > >- Tom Hales, in 'Jordan's Proof of the Jordan Curve Theorem'. > >"We say that Gamma is a curve if it is the image in >the plane or in space of an interval [a, b] of real >numbers o

Re: Measuring Fractal Dimension ?

David C. Ullrich writes: > >> obviously converges to f, but not uniformly. On a closed interval, > >> any continuous function is uniformly continuous. > > > >Isn't (-?, ?) closed? > > What is your version of the definition of "closed"? I think the whole line is closed, but I hadn't realized any

Re: Measuring Fractal Dimension ?

also called a Jordan curve, is the image of a continuous one-to-one function from R/Z to R2. [...]" - Tom Hales, in 'Jordan's Proof of the Jordan Curve Theorem'. "We say that Gamma is a curve if it is the image in the plane or in space of an interval [a, b] of real numbers of a

Re: Measuring Fractal Dimension ?

David C. Ullrich writes: > On Wed, 17 Jun 2009 08:18:52 -0700 (PDT), Mark Dickinson > wrote: > >>On Jun 17, 3:46 pm, Paul Rubin wrote: >>> Mark Dickinson writes: >>> > It looks as though you're treating (a portion of?) the Koch curve as >>> > the graph of a functi

Re: Measuring Fractal Dimension ?

On Jun 18, 2009, at 2:19 PM, David C. Ullrich wrote: On Wed, 17 Jun 2009 07:37:32 -0400, Charles Yeomans wrote: On Jun 17, 2009, at 2:04 AM, Paul Rubin wrote: Jaime Fernandez del Rio writes: I am pretty sure that a continuous sequence of curves that converges to a continuous curve, will

Re: Measuring Fractal Dimension ?

On Wed, 17 Jun 2009 08:18:52 -0700 (PDT), Mark Dickinson wrote: >On Jun 17, 3:46 pm, Paul Rubin wrote: >> Mark Dickinson writes: >> > It looks as though you're treating (a portion of?) the Koch curve as >> > the graph of a function f from R -> R and claiming that f

Re: Measuring Fractal Dimension ?

On Wed, 17 Jun 2009 07:37:32 -0400, Charles Yeomans wrote: > >On Jun 17, 2009, at 2:04 AM, Paul Rubin wrote: > >> Jaime Fernandez del Rio writes: >>> I am pretty sure that a continuous sequence of >>> curves that converges to a continuous curve, will do so uniformly. >> >> I think a typical exam

Re: Measuring Fractal Dimension ?

; I don't think any countable set, even a countably-infinite set, can have >>>> a fractal dimension. It's got to be uncountably infinite, and therefore >>>> uncomputable. >>> >>> I think the idea is you assume uniform continuity of the set (as &g

Re: Measuring Fractal Dimension ?

On Wed, 17 Jun 2009 14:50:28 +1200, Lawrence D'Oliveiro wrote: >In message <7x63ew3uo9@ruckus.brouhaha.com>, wrote: > >> Lawrence D'Oliveiro writes: >> >>> I don't think any countable set, even a countably-infinite set, can have >>>

Re: Measuring Fractal Dimension ?

On Wed, 17 Jun 2009 14:50:28 +1200, Lawrence D'Oliveiro wrote: >In message <7x63ew3uo9@ruckus.brouhaha.com>, wrote: > >> Lawrence D'Oliveiro writes: >> >>> I don't think any countable set, even a countably-infinite set, can have >>>

Re: Measuring Fractal Dimension ?

On Wed, 17 Jun 2009 14:50:28 +1200, Lawrence D'Oliveiro wrote: >In message <7x63ew3uo9@ruckus.brouhaha.com>, wrote: > >> Lawrence D'Oliveiro writes: >> >>> I don't think any countable set, even a countably-infinite set, can have >>>

Re: Measuring Fractal Dimension ?

On Jun 17, 4:18 pm, Mark Dickinson wrote: > On Jun 17, 3:46 pm, Paul Rubin wrote: > > > Mark Dickinson writes: > > > It looks as though you're treating (a portion of?) the Koch curve as > > > the graph of a function f from R -> R and claiming that f is > > > uniform

Re: Measuring Fractal Dimension ?

On Jun 17, 3:46 pm, Paul Rubin wrote: > Mark Dickinson writes: > > It looks as though you're treating (a portion of?) the Koch curve as > > the graph of a function f from R -> R and claiming that f is > > uniformly continuous.  But the Koch curve isn't such a graph (

Re: Measuring Fractal Dimension ?

On Jun 17, 2:18 pm, pdpi wrote: > On Jun 17, 1:26 pm, Jaime Fernandez del Rio > wrote: > > > P.S. The snowflake curve, on the other hand, is uniformly continuous, right? > > The definition of uniform continuity is that, for any epsilon > 0, > there is a delta > 0 such that, for any x and y, if x-

Re: Measuring Fractal Dimension ?

On Jun 17, 1:26 pm, Jaime Fernandez del Rio wrote: > On Wed, Jun 17, 2009 at 1:52 PM, Mark Dickinson wrote: > > Maybe James is thinking of the standard theorem > > that says that if a sequence of continuous functions > > on an interval converges uniformly then its limit > > is continuous? s/James

Re: Measuring Fractal Dimension ?

On Wed, Jun 17, 2009 at 1:52 PM, Mark Dickinson wrote: > Maybe James is thinking of the standard theorem > that says that if a sequence of continuous functions > on an interval converges uniformly then its limit > is continuous? Jaime was simply plain wrong... The example that always comes to mind

Re: Measuring Fractal Dimension ?

On Jun 17, 7:04 am, Paul Rubin wrote: > I think a typical example of a curve that's continuous but not > uniformly continuous is > >    f(t) = sin(1/t), defined when t > 0 > > It is continuous at every t>0 but wiggles violently as you get closer > to t=0.  You wouldn'

Re: Measuring Fractal Dimension ?

On Jun 17, 2009, at 2:04 AM, Paul Rubin wrote: Jaime Fernandez del Rio writes: I am pretty sure that a continuous sequence of curves that converges to a continuous curve, will do so uniformly. I think a typical example of a curve that's continuous but not uniformly continuous is f(t) = s

Re: Measuring Fractal Dimension ?

Jaime Fernandez del Rio writes: > I am pretty sure that a continuous sequence of > curves that converges to a continuous curve, will do so uniformly. I think a typical example of a curve that's continuous but not uniformly continuous is f(t) = sin(1/t), defined when t > 0 It is continuous at

Re: Measuring Fractal Dimension ?

On Wed, Jun 17, 2009 at 4:50 AM, Lawrence D'Oliveiro wrote: > In message <7x63ew3uo9@ruckus.brouhaha.com>,  wrote: > >> Lawrence D'Oliveiro writes: >> >>> I don't think any countable set, even a countably-infinite set, can have >>> a fr

Re: Measuring Fractal Dimension ?

In message <7x63ew3uo9@ruckus.brouhaha.com>, wrote: > Lawrence D'Oliveiro writes: > >> I don't think any countable set, even a countably-infinite set, can have >> a fractal dimension. It's got to be uncountably infinite, and therefore >> unco

Re: Measuring Fractal Dimension ?

On 15 Jun 2009 04:55:03 GMT, Steven D'Aprano wrote: >On Sun, 14 Jun 2009 14:29:04 -0700, Kay Schluehr wrote: > >> On 14 Jun., 16:00, Steven D'Aprano >> wrote: >> >>> Incorrect. Koch's snowflake, for example, has a fractal dimension of >>&g

Re: Measuring Fractal Dimension ?

Lawrence D'Oliveiro writes: > I don't think any countable set, even a countably-infinite set, can have a > fractal dimension. It's got to be uncountably infinite, and therefore > uncomputable. I think the idea is you assume uniform continuity of the set (as expressed

Re: Measuring Fractal Dimension ?

On Jun 15, 5:55 am, Steven D'Aprano wrote: > On Sun, 14 Jun 2009 14:29:04 -0700, Kay Schluehr wrote: > > On 14 Jun., 16:00, Steven D'Aprano > > wrote: > > >> Incorrect. Koch's snowflake, for example, has a fractal dimension of > >> log 4/l

Re: Measuring Fractal Dimension ?

On Sun, 14 Jun 2009 14:29:04 -0700, Kay Schluehr wrote: > On 14 Jun., 16:00, Steven D'Aprano > wrote: > >> Incorrect. Koch's snowflake, for example, has a fractal dimension of >> log 4/log 3 ≈ 1.26, a finite area of 8/5 times that of the initial >> triangle

Re: Measuring Fractal Dimension ?

>> In message , Peter Billam wrote: >>> Are there any modules, packages, whatever, that will >>> measure the fractal dimensions of a dataset, e.g. a time-series ? > Lawrence D'Oliveiro wrote: >> I don't think any countable set, even a countably-infinite

Re: Measuring Fractal Dimension ?

On 14 Jun., 16:00, Steven D'Aprano wrote: > Incorrect. Koch's snowflake, for example, has a fractal dimension of log > 4/log 3 ≈ 1.26, a finite area of 8/5 times that of the initial triangle, > and a perimeter given by lim n->inf (4/3)**n. Although the perimeter is >

Re: Measuring Fractal Dimension ?

Lawrence D'Oliveiro wrote: > In message , Peter Billam wrote: > >> Are there any modules, packages, whatever, that will >> measure the fractal dimensions of a dataset, e.g. a time-series ? > > I don't think any countable set, even a countably-infinite set, ca

Re: Measuring Fractal Dimension ?

Arnaud Delobelle writes: > I think there are attempts to estimate the fractal dimension of a set > using a finite sample from this set. But I can't remember where I got > this thought from! There are image data compression schemes that work like that, trying to detect self-sim

Re: Measuring Fractal Dimension ?

Lawrence D'Oliveiro writes: > In message , Peter Billam wrote: > >> Are there any modules, packages, whatever, that will >> measure the fractal dimensions of a dataset, e.g. a time-series ? > > I don't think any countable set, even a countably-infinite set, can

Re: Measuring Fractal Dimension ?

In message , Peter Billam wrote: > Are there any modules, packages, whatever, that will > measure the fractal dimensions of a dataset, e.g. a time-series ? I don't think any countable set, even a countably-infinite set, can have a fractal dimension. It's got to be uncountab

Measuring Fractal Dimension ?

Greetings. Are there any modules, packages, whatever, that will measure the fractal dimensions of a dataset, e.g. a time-series ? Like the Correlation Dimension, the Information Dimension, etc... Peter -- Peter Billam www.pjb.com.auwww.pjb.com.au/comp/contact.html -- http

Re: Fractal curve

Steve Heyburn wrote: > Hello there, > > I am studying programming at University and we are basing the course on > Python. > We are currently looking at fractal curves and I was wondering if you could > email me code for a dragon curve please, or a similar fractal

Fractal curve

Hello there, I am studying programming at University and we are basing the course on Python. We are currently looking at fractal curves and I was wondering if you could email me code for a dragon curve please, or a similar fractal curve.   Thank you Steve -- http://mail.python.org/mailman